Arcs & Angles in Circles Worksheet

Sample problems

A central angle equals the measure of its intercepted arc. An inscribed angle equals half its intercepted arc. For a circle of radius $r$, an arc with central angle ${\theta }^{\circ }$ has arc length $\frac{\theta }{360}\cdot 2\pi r$, and a sector with that angle has area $\frac{\theta }{360}\cdot \pi r^2$. Leave arc-length and sector-area answers in terms of $\pi$.

1. 1. A central angle of a circle measures $72^{\circ }$. What is the measure of its intercepted arc?
2. 2. An inscribed angle intercepts an arc of $130^{\circ }$. Find the measure of the inscribed angle.
3. 3. An inscribed angle measures $40^{\circ }$. Find the measure of the arc it intercepts.
4. 4. In the circle, $O$ is the center. Find the measure of arc $AB$.

Plus 10 more problems and a full answer key in the PDF.